Q. Assume that the economy wide expected future marginal product of capital is MPKf = 20 - 0.02K, where K is the future capital stock. The depreciation rate of capital, d, is 20% every period. The current capital stock is 900 units of capital. The price of a unit of capital is 1 unit of output. Industries pay taxes equal to 50% of their output. The consumption function of the economy is Cd = 100 + 0.5Y - 200r, where Cd is desired consumption; Y is output also r is the real interest rate. Government purchases equal 200 also full employment output is 1000.

a. Assume that the real interest rate is 10% every period. Illustrate what are the values of the tax-adjusted utilize cost of capital, the desired future capital stock also the desired level of investment? Explain your answers.

b. Now consider the real interest rate concluded by goods marketplace equilibrium. The subsequent parts of the problem will guide you to this interest rate.

i. Write the tax-adjusted utilize cost of capital as a function of the real interest rate r. Also write the desired future capital stock also desired investment as functions of r.

ii. Utilize the investment function derived in part (i) along with the consumption function also government purchases to compute the real interest rate that clears the goods marketplace. Illustrate what are the goods marketplace-clearing values of desired consumption, desired saving also desired investment? Illustrate what are the tax-adjusted utilize cost of capital also the desired capital stock in this equilibrium? Explain your answers.